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              <text> The creation of Rivet analysis plugins for LHCB_2012_I1089993 and LHCB_2011_I1082369; it was found that in the first paper, the rapidity folding gave a smaller standard deviation of 15.4% difference but similar average error, 0.9%, than if it were to not be included. Furthermore, the optimal histogram scaling had an extra factor of 1/2 , while in the next paper, they had factors of 2 for tables 1 and 3 but 5 and 6 were found to need 3/2 - the rest have 3. These used the simulator Pythia8. Later on, tools were created to better compare the event generator EvtGen in Python, which found the reduced χ^2-statistic.</text>
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              <text>As the adoption of Large Language Models (LLMs) is becoming ubiquitous, understanding their pitfalls is becoming increasingly urgent. LLMs are known to hallucinate and may be subject to cascading hallucinatory generations due to their autoregressive structure and exposure bias. This paper first introduces the topic of hallucination cascade, covering relevant literature. Then an experiment is presented on the propagation of hallucination through long answer text generation, for all combinations of five LLMs - Qwen2 (0.5B), Qwen2 (7B), Llama3.1 (8B), Gemma2 (9B) and Mistral-NeMo (12B) - at five levels of temperature: 0, 0.75, 1, 1.25, 2. In a novel methodology, responses are generated by the five LLMs, then labelled by two more LLMs as hallucinatory or not on both a token and sentence level. The labelling is done with clear instructions and additional context to ensure its quality. Correlational evidence was found on both granularity levels that hallucinatory tokens are positively autocorrelated at lag 1, and that autocorrelation monotonically decreases as lag increases (token level only), supporting the cascading hallucination hypothesis. Finally, some hallucination mitigating techniques are presented, with both research and application in mind. All the code used for the empirical part of this paper (Section 3) can be found at https://github.com/LucMekouar/URSS_2024.</text>
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              <text>This study expands upon the work of Barberis (2012) which discusses the application of Tversky and Kahneman’s updated model of prospect theory in 1992 (cumulative prosepect theory) to the area of repeated bets with win probabilities of close to 0.5, in contexts such as casinos or financial markets. In particular, we look to explore the idea of a ’time inconsistency’ that is abundant in many strategic situations evaluated using cumulative prospect theory. What this refers to is the phenomenon of an agent deciding what their optimal strategy is before entering the situation but then following a different plan of action at future time periods. We explore the impacts of moving away from simple bets by changing some of the underlying principles, such as the effects of generalising the win probability, p, or introducing a random shock to the reward at a random point in time. This allows us to connect Barberis’ work to areas beyond just a casino, such as prices of securities in financial markets. We will do this by exploring the effects on a two-period binomial model but which can be extended.</text>
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